PHYSICAL REVIEW B 72, 014412 共2005兲
Martensitic transitions and the nature of ferromagnetism in the austenitic and martensitic states
of Ni- Mn- Sn alloys
Thorsten Krenke, Mehmet Acet,* and Eberhard F. Wassermann
Fachbereich Physik, Experimentalphysik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
Xavier Moya, Lluís Mañosa, and Antoni Planes
Facultat de Física, Departament d’Estructura i Constituents de la Materìa, Universitat de Barcelona, Diagonal 647,
E-08028 Barcelona, Catalonia, Spain
共Received 24 November 2004; revised manuscript received 1 February 2005; published 5 July 2005兲
Structural and magnetic transformations in the Heusler-based system Ni0.50Mn0.50−xSnx are studied by x-ray
diffraction, optical microscopy, differential scanning calorimetry, and magnetization. The structural transformations are of austenitic-martensitic character. The austenite state has an L21 structure, whereas the structures
of the martensite can be 10M, 14M, or L10 depending on the Sn composition. For samples that undergo
martensitic transformations below and around room temperature, it is observed that the magnetic exchange in
both parent and product phases is ferromagnetic, but the ferromagnetic exchange, characteristic of each phase,
is found to be of different strength. This gives rise to different Curie temperatures for the austenitic and
martensitic states.
DOI: 10.1103/PhysRevB.72.014412
PACS number共s兲: 75.50.Cc, 81.30.Kf
I. INTRODUCTION
The martensitic transformation is a first-order solid-solid
phase transition, which takes place by the diffusionless
shearing of the parent austenitic phase. The main characteristics of a first-order martensitic phase transformation are the
presence of supercooled and superheated states that lead to a
thermal hysteresis of width ⌬T. The characteristic temperatures related to the martensitic transformation are the martensite start temperature M s, martensite finish temperature M f ,
austenite start temperature As, and the austenite finish temperature A f . The martensitic transformation has broad applications, among which steel hardening and shape memory
devices are of prime importance. One understands under the
so-called shape memory effect the capability of a material to
remember its original shape when it is deformed in the martensitic state and then heated to retransform to the austenitic
state. One of the earliest known shape memory alloys is
Au52.5Cd47.5.1 Since then, many other systems were found,
among which Ni- Ti has the widest application.
The austenite-martensite transformation in shape memory
alloys is thermoelastic, which is a property characterized by
a narrow thermal hysteresis of several ten Kelvins or less.
This implies that the dissipative contribution to the free energy during the transformation is small, so that the deformation energy is essentially elastically stored in the twin morphology of the martensite structure.2 The two components of
the twin have the same crystal structure, but different orientations, and are known as variants. The variants build selfaccommodating groups with other twins such that they minimize the elastic contribution to the free energy.
Some Heusler based alloys, such as Cu- Ni- Al, Cu- ZnAl, etc., also exhibit the shape memory effect. The stoichiometric Heusler compound X2YZ crystallizes in the L21 structure 共space group Fm3m兲, which is made up of four interpenetrating fcc sublattices. Each sublattice is occupied by
1098-0121/2005/72共1兲/014412共9兲/$23.00
one sort of atom. If the alloy transforms martensitically, the
structure at T ⬍ M s usually has a modulated structure.
In the case when the Heusler alloy is magnetic, it can
exhibit the magnetic shape memory 共MSM兲 effect. This occurs especially when the Y species is Mn, but other transition
elements are also possible. In these alloys, an external magnetic field can induce large strains when applied in the martensitic state.3,4 In Ni2MnGa, these strains can be as large as
10% in a field of about 1 T. The field-induced strain is due to
the reorientation of the tetragonal martensite variants by twin
boundary motion. The driving force for the reorientation is
provided by the difference in the Zeeman energy ⌬M · H of
neighboring variants.5 The maximum achievable strain ⑀max
depends on the tetragonality c / a of the martensitic phase.6
Depending on the composition of the Ni- Mn- Ga alloy, the
martensitic phase occurs as various modulated phases such
as 10M, 14M, or L10.7 Although Ni- Mn- Ga alloys offer
large magnetic field-induced strains, they are brittle which
makes it difficult for applications. Therefore, in the past few
years, there has been more research invested in the search for
materials exhibiting the MSM effect and having more favorable mechanical properties at the same time. Over the past
few years, other MSM alloys, such as Fe- Pt,8 Fe- Pd,9 CoNi- Al,10 Co- Ni- Ga,11 Fe- Ni- Ga,12 and Ni- Mn- Al,13–16
have been encountered.
Ni- Mn- Ga and Ni- Mn- Al are isoelectronic at equal Ga
and Al concentrations when the Ni and Mn contents are kept
fixed. Close to the stoichiometric Heusler composition, they
are ferromagnetic 共FM兲 in the L21 parent phase and undergo
a martensitic transformation at temperatures below their respective Curie temperatures TC exhibiting MSM
properties.17,18
One also observes martensitic transformations in NiMn-Z Heusler alloys where Z can be a group III or group IV
element such as In, Sn, or Sb, namely other than Ga or Al.19
In a considerable region around the stoichiometric Heusler
014412-1
©2005 The American Physical Society
PHYSICAL REVIEW B 72, 014412 共2005兲
KRENKE et al.
TABLE I. Compositions of the Ni0.50Mn0.50−xSnx samples determined by EDX analysis and the valence electron concentrations per
atom e / a determined as the concentration-weighted sum of s, d, and
p electrons.
x
Ni
Mn
Sn
e/a
0.25
0.20
0.18
0.15
0.13
0.10
0.05
49.6
50.5
49.5
50.1
49.9
49.5
49.8
24.9
29.2
32.3
34.5
37.1
40.4
45.1
25.5
20.3
18.2
15.4
13.0
10.1
5.1
7.723
7.906
7.939
8.041
8.107
8.182
8.341
composition, the structure of Ni2MnSn can be L21 and DO3.
The binaries Ni- Mn and Ni- Sn undergo martensitic transformations, whereby the product phases are tetragonal and hexagonal, respectively. As Sn or Mn is added to these binaries
as the third element to form the ternary Ni- Mn- Sn, the presence of a martensitic transformation persists up to around
10 at. % substitute atom. The alloy series Ni0.50Mn0.50−xSnx
with 0.05艋 x 艋 0.25 is particularly interesting in relation to
structural and magnetic properties. In this work, we present a
study on the structural properties and the nature of the magnetic coupling in the parent and product phases of this series.
The aim is to provide an understanding of the basic properties of martensitic transformations in these alloys.
II. EXPERIMENT
Ingots of about 3 g were prepared by arc-melting the pure
metals under argon atmosphere in a water-cooled Cu crucible. They were remelted several times. The ingots were
subsequently encapsulated under argon in quartz glass and
annealed at 1273 K for 2 h. They were then quenched in ice
water. The compositions of the Ni0.50Mn0.50−xSnx alloys were
determined by energy dispersive x-ray analysis 共EDX兲 and
are collected in Table I. The corresponding valence electron
concentration e / a 共electrons per atom兲 is also given in the
table. This is calculated as the concentration weighted sum of
the number of 3d and 4s electrons of Ni and Mn and the
number of 4s and 4p electrons of Sn.
Polycrystalline samples of 30– 100 mg cut from the ingots using a low speed diamond saw were used as samples
for magnetization and calorimetric studies. For the differential scanning calorimetry 共DSC兲 measurements, one side of
the samples were ground down to 1200 grit SiC abrasive to
insure proper thermal contact. Calorimetric measurements
were carried out in the temperature range 100 K 艋 T
艋 830 K in a modulated DSC 共TA Instruments MDSC 2920兲,
which can be operated in both standard DSC and modulated
modes. For standard DSC measurements, the cooling and
heating rates were 2 – 5 K / min. We have also used a separate
high sensitivity calorimeter to determine the entropy change
of the martensitic transformation in the temperature range
100 K 艋 T 艋 350 K. Typical cooling and heating rates in
these measurements were 0.5 K / min.
FIG. 1. 共a兲 ZFC, FC, and FH M共T兲 of the samples with x
= 0.25 and 0.20 in H = 50 Oe. The inset, with a higher resolution in
the vertical scale, highlights the splitting of the ZFC and FC curves
for x = 0.20. M in the inset is in units of emu g1 共b兲 M共H兲 of the
sample with x = 0.25. Prior to each M共H兲 measurement, the samples
were prepared in the ZFC state by bringing them above 380 K.
The temperature dependence of the magnetization M共T兲
in a low external magnetic field 共H = 50 Oe兲 was measured in
the temperature range 5 K 艋 T 艋 380 K using a superconducting quantum interference device magnetometer. Prior to
the measurements, the sample was prepared in a zero-fieldcooled state 共ZFC兲 by cooling it from 380 to 5 K in the absence of a magnetic field. Subsequently, the external field
was applied and the measurements were taken on increasing
temperature up to 380 K. Then, without removing the external field, the measurement was made on decreasing temperature, i.e., field-cooled 共FC兲. As a last step, again without
removing the external field the magnetization was measured
on increasing temperature. The last step is denoted as the
field-heated 共FH兲 sequence. Any hysteresis in the FC-FH sequence is expected to be associated with a structural transition, whereas any splitting of the ZFC and FC curves below
the ferromagnetic transition temperatures is expected to be
associated with coexisting antiferromagnetic 共AF兲 exchange.
To further characterize the magnetic properties, the magnetic
field dependence of the magnetization M共H兲 was measured
in fields up to 50 kOe.
Room temperature structural analysis was carried out with
conventional x-ray techniques using Cu K␣ radiation, and
the microstructure of the specimens was examined by optical
microscopy. For these studies, the samples were polished and
subsequently etched in Oberhoffer solution 共1 g CuCl2, 30 g
FeCl3, 0.5 g SnCl2, 42 ml HCl, 500 ml H2O, and 500 ml
C2H5OH兲.
III. RESULTS
A. Magnetization studies
M共T兲 and M共H兲 for all samples are presented in Figs.
1–5. Figure 1共a兲 shows M共T兲 for the sample with x = 0.20 and
for the sample with stoichiometric composition x = 0.25. The
behavior of M共T兲 for the sample with x = 0.25 is that of a
typical ferromagnet with a Curie temperature TC = 340 K.
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MARTENSITIC TRANSITIONS AND THE NATURE OF…
FIG. 2. 共a兲 ZFC, FC, and FH M共T兲 of the sample x = 0.18 in
H = 50 Oe. The inset, with a higher resolution in the vertical scale,
highlights the splitting of the ZFC and FC curves. 共b兲 M共H兲 at 5 K
of the samples x = 0.25, 0.20, and 0.18. Prior to each M共H兲 measurement the samples were prepared in the ZFC state by bringing
them above 380 K.
Even in a low external magnetic field of 50 Oe, the FC curve
retraces the ZFC curve at a magnetization value corresponding to the demagnetizing limit of the sample. The FH curve
also retraces the FC and ZFC curves. M共H兲 data at various
temperatures are given in Fig. 1共b兲. The magnetization saturates at low temperatures, and at 300 K 共close to TC兲 the
saturation weakens leading to a finite high field susceptibility. The M共H兲 data at 370 K, which corresponds to the paramagnetic state, is initially linear. However, at higher fields,
the data deviate from linearity due to the presence of short
range FM correlations.
As Mn is substituted for Sn, excess Mn atoms occupy Sn
sites. In such spatial configurations, Mn atoms can have Mn
atoms as nearest neighbors along the 关110兴 directions. The
Mn- Mn spacing, in this case, is smaller than that in the
stoichiometric compound, and is, therefore, expected to in-
FIG. 3. 共a兲 ZFC, FC, and FH M共T兲 of the sample with x = 0.15 in
H = 50 Oe. 共b兲 M共T兲 plotted in a temperature range around the martensitic transition. 共c兲 M共H兲 at 5, 160, 195, 220, and 350 K. Prior to
each M共H兲 measurement, the samples were prepared in the ZFC
state by bringing them above 380 K.
FIG. 4. 共a兲 ZFC, FC, and FH M共T兲 of the sample with x = 0.13 in
H = 50 Oe. 共b兲 M共T兲 plotted in a temperature range around the martensitic transition. 共c兲 M共H兲 at 5, 150, 275, 300, 306, and 330 K.
Prior to each M共H兲 measurement, the samples were prepared in the
ZFC state by bringing them above 380 K.
troduce AF exchange leading to local noncollinear spin
structures,20,21 which can pin the FM domains in different
configurations depending on whether the sample is cooled
through TC in an external field or not. The different configurations cause a separation of the FC and ZFC curves just
below the Curie temperature.22,23 The separation is found
below TCA for the samples in the concentration range 0.13
艋 x 艋 0.20. For clarity, we show this only for the samples
FIG. 5. 共a兲 ZFC, FC, and FH M共T兲 for x = 0.10 and 共b兲 M共H兲 at
100 and 350 K. 共c兲 ZFC, FC, and FH M共T兲 for x = 0.05 and 共d兲
M共H兲 at 5 and 100 K.
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PHYSICAL REVIEW B 72, 014412 共2005兲
KRENKE et al.
with x = 0.20 and 0.18 in the inset of Figs. 1共a兲 and 2共a兲. In
this composition range, TC is nearly the same as that of the
stoichiometric compound.
A further effect related to the introduction of AF exchange
as the Sn concentration is reduced can also be identified in
Fig. 2共b兲 where M共H兲 at 5 K of the samples with x
= 0.18– 0.25 are compared. Whereas saturation is attained for
x = 0.25 somewhat above 15 kOe, M共H兲 of x = 0.20 and x
= 0.18 do not saturate, even at 5 K, owing to the presence of
AF exchange. Furthermore, M共H兲 in high fields decreases
with decreasing Sn concentration.
As the Sn concentration is further decreased, we reach the
situation shown in Fig. 3共a兲, where M共T兲 is plotted for the
sample with x = 0.15. This sample is FM below TCA = 320 K. A
splitting between the ZFC and FC magnetization data 关Fig.
3共b兲兴, occurs just below TCA as in the data for the x = 0.20 and
0.18 samples. The ferromagnetism extends down to about
190 K, below which the magnetization rapidly decreases. In
the vicinity of this temperature, the FH data do not retrace
the FC data but show a narrow hysteresis 关Fig. 3共c兲兴. When
considered together with the results of the calorimetric measurements presented under Sec. III B, the hysteresis can be
attributed to a first-order structural transition. The forward
and reverse transition temperatures have been determined by
DSC measurements and are indicated with arrows. The splitting between the ZFC and FC data in the martensitic state
becomes much more pronounced than that just below TCA.
Evidently, the distortion of the lattice in the martensitic state
has considerable effect on the pinning of the spin configurations caused by the AF exchange. As can be seen from the
M共H兲 data given at various temperatures in Fig. 3共d兲, the
sample is in a FM state also below M s = 189 K. The magnitude of the magnetization at temperatures lower than M s is
smaller than at higher temperatures. These points are further
discussed in Sec. IV.
M共T兲 and M共H兲 for x = 0.13 are plotted in Fig. 4. These
data exhibit a number of features associated with a first-order
structural transformation and two magnetic transitions. Here
also, the structural transition temperatures are those determined from the DSC measurements 关Fig. 4共b兲兴. At high temperatures, in the austenitic state, the sample is paramagnetic
and orders ferromagnetically below TCA = 311 K 关Fig. 4共a兲兴.
The M共H兲 curve at 330 K in Fig. 4共c兲 is linear up to about
5 kOe, after which it acquires a curvature due to the presence
of ferromagnetic short range correlations—330 K being
close to TCA. At 306 K, which is just below TCA, M共H兲 initially
rises rapidly as expected for a ferromagnet. Afterwards, the
rate of increase decreases, and a saturation value is not approached. The coexistence of AF exchange within the FM
matrix due to excess Mn in the crystal structure is the essential source for nonsaturation. The presence of AF exchange is
further evidenced by the different temperature behavior of
the FC and ZFC curves beginning just below TCA.
At M s = 307 K, slightly below TCA, a martensitic transformation takes place. As seen in Fig. 4共a兲, and more detailed in
Fig. 4共b兲, the martensitic transformation is identified by the
hysteresis in the FC and FH M共T兲 curves occurring in a
narrow temperature interval just below TCA. For temperatures
lower than M f , M共T兲 of the FC and FH measurement se-
quences retrace. The calorimetric data presented in Sec. III B
also confirm the presence for this first-order structural transition. Below M s, the magnetization decreases with decreasing temperature as seen in Fig. 4共b兲. The decrease is an indication that the martensitic state does not sustain long range
ferromagnetism at these temperatures. This property is also
observed in M共H兲 关Fig. 4共c兲兴. M共H兲 in high external fields
drops progressively as the temperature decreases from
306 to 300 K, and finally to 275 K. With decreasing temperature, the proportion of martensite increases, and the effect of ferromagnetic exchange of the austenite phase weakens. At 275 K, the characteristics of the M共H兲 data indicate
that long-range ferromagnetism vanishes, and the form of the
M共H兲 curve resembles more that for 330 K. There is no
longer a rapid initial rise of M共H兲 as for the data at 300 K. It
is not possible to determine from the present data what the
exact nature of the magnetic coupling is at these temperatures. Further studies with neutron techniques would be required to understand this aspect of the problem.
As the temperature decreases, a second magnetic transition is observed at TCM = 230 K, where the magnetic state of
the martensitic phase becomes ferromagnetic 关Fig. 4共a兲兴.
There is no essential difference in M共T兲 of the FC and FH
states indicating that the structural transformation is essentially complete at these temperatures. On the other hand, the
separation in M共T兲 between the FC and ZFC states below
TCM = 230 K is much more pronounced than that at TCA, as in
the case of the sample with x = 0.15. This shows that AF
exchange persists at these temperatures, as can also be seen
in the nonsaturating property of M共H兲 at temperatures below
150 K shown in Fig. 4共c兲.
At lower Sn concentrations, long range FM ordering
weakens appreciably. This can be seen in the M共T兲 and
M共H兲 data for the samples with x = 0.10 and 0.05 in Fig. 5.
The magnetizations of these samples in 50 Oe 关Figs. 5共a兲 and
5共c兲兴 are three to four orders of magnitude smaller than in the
case for the samples with well-defined FM ground states.
The FC M共T兲 data for x = 0.10 关Fig. 5共a兲兴 exhibits a broad
magnetic transition over more than 100 K in spite of the
small external measuring field of 50 Oe. The Curie temperature of this transition is at about 137 K; close to the temperature where the splitting occurs. The splitting of the FC and
ZFC curves indicates that considerable AF exchange is
present. The FM character is also evidenced by the M共H兲
data at 100 K in Fig. 5共b兲. At temperatures above TCM , M共H兲
shows a linear behavior at high temperatures, whereas below
this temperature, the curve is nonlinear and exhibits a small
coercivity in the hysteresis.
The values of M共T兲 for x = 0.10 关Fig. 5共c兲兴 are an order of
magnitude smaller than those for x = 0.10. M共H兲 is also linear
at low and high temperatures, as seen in Fig. 5共d兲, indicating
that ferromagnetism is no longer present at this concentration. At such high Mn concentrations, one would rather expect AF exchange to predominate, which would account for
the linearity of M共H兲. In spite of predominating antiferromagnetism in this sample, a splitting is still found between
the ZFC and FC data in Fig. 5共c兲 suggesting that the sample
is magnetically inhomogeneous.
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MARTENSITIC TRANSITIONS AND THE NATURE OF…
FIG. 6. dQ / dT vs temperature for the alloys
undergoing martensitic transformations 共a兲 x
= 0.15, 共b兲 x = 0.13, 共c兲 x = 0.10, and 共d兲 x = 0.05.
B. Calorimetric studies
In order to characterize the martensitic transformation in
more detail, we have studied the thermal properties of
Ni0.50Mn0.50−xSnx by DSC. For the alloys with x 艌 0.18, no
structural transformation has been observed.
The results of calorimetric studies for the alloys 0.05艋 x
艋 0.15 are plotted in Figs. 6共a兲–6共d兲, where the heating and
cooling cycles are shown by the arrows. These samples exhibit a first-order structural transformation, for which M s increases with decreasing Sn concentration. We collect in
Table II the transition temperatures M s, M f , As, and A f and
the width of the hysteresis ⌬T determined as the difference
between the temperatures corresponding to the peak positions. A further feature is observed at TCA for x = 0.15 in Fig.
6共a兲. This feature is not observable for x = 0.13 because of the
close-lying TCA and M s temperatures. The entropy and enthalpy changes 共⌬S and ⌬H, respectively兲 around the structural transitions are calculated from the baseline corrected
calorimetry data using the relationships
⌬H =
冕 冉 冊冉 冊
Tf
Ti
and
⌬S =
dQ
dt
dT
dt
−1
冕 冉 冊冉 冊
Tf
Ti
1 dQ
T dt
dT
dt
共1兲
dT
−1
共2兲
dT,
where Ti and T f are the initial and final temperature limits of
integration. The values of ⌬H and ⌬S are also included in
Table II. In the cooling experiments in Fig. 6共d兲, additional
peaks appear in the heat flow that are related to the transformation kinetics. Various martensitic structures can be identified which are found in the x-ray spectra in the next section.
C. Structural properties
Figure 7 shows an x-ray diffraction pattern taken at room
temperature for the alloys with x = 0.25 and 0.15. The superstructure reflections with the Miller indices h, k, l = 2n + 1 are
also observed implying that the patterns are related to the
L21 phase. By replacing Sn with Mn, which has a smaller
atomic radius, the lattice constants of the austenitic phase
becomes smaller, and the peak positions shift to larger
angles. At room temperature, the alloys with x 艋 13 are martensitic, in agreement with the calorimetric measurements.
However, the structure of the martensite changes as the Mn
concentration is varied as seen in Figs. 8–10. Figure 8 shows
the diffraction pattern of the alloy with x = 0.13. The reflections can be attributed to the 10M modulated martensite
structure. The diffraction pattern of the alloy with x = 0.10
共Fig. 9兲 is related to that of a 14M martensitic structure. The
inset of Fig. 9 shows the details in the range 38° 艋 2␪
艋 46°. The unit cell is monoclinic making an angle ␤
= 93.84°. For x = 0.05, the martensite has an unmodulated
double tetragonal L10 structure as determined from the spectrum in Fig. 10. Such structures are also observed in NiMn- Ga alloys. The results of the x-ray diffraction experiments are collected in Table III. Three of the studied alloys
are in the martensitic phase at room temperature.
TABLE II. Structural transition temperatures and the associated characteristic thermal parameters.
x
M s 共K兲
M f 共K兲
As 共K兲
A f 共K兲
⌬T 共K兲
⌬H 共J mol−1兲
⌬S 共J mol−1 K−1兲
0.15
0.13
0.10
0.05
189
307
444
711
174
289
437
693
190
295
445
718
202
318
453
743
19
19
10
31
313± 53
911± 65
1642± 63
3060± 360
1.66± 0.13
3.0± 0.3
3.7± 0.2
4.3± 0.7
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KRENKE et al.
FIG. 7. X-ray diffraction pattern at room temperature for x
= 0.25 共lower兲 and x = 0.15 共upper兲. The crystal structure is in both
cases L21.
The variation of the crystal structure at room temperature
from L21 to the modulated structures 10M, to 14M, and then
to L10, as the Sn concentration decreases, can also be seen in
the microstructure of the alloys shown in Figs. 11共a兲–11共d兲.
These are optical microscopy images of the surface of the
alloys with x = 0.05, 0.10, 0.13, and 0.25. Figure 11共a兲 shows
the surface of the sample with x = 0.25, for which the grain
size varies in the range 50– 300 ␮m. The black spots are
voids caused by the etching during surface preparation.
Figures 11共b兲–11共d兲 show the microstructure of the
samples that are martensitic at room temperature. No phase
separation can be identified. This is also in agreement with
the x-ray diffraction patterns, where all reflections are related
to the martensitic phases. The grain size lies within the range
50– 300 ␮m. The morphologies of the 10M, 14M, and the
unmodulated phases appear to be different from one another.
Although in all three cases the martensite is platelike, which
can be recognized by the linear grain boundary of each plate,
the widths of the twins are different for 10M, 14M, and L10.
For 10M martensite, a broad form is found, whereas for 14M
martensite, the form is finer, and that of the unmodulated
FIG. 8. X-ray diffraction pattern at room temperature for x
= 0.13. The crystal structure is 10M with an orthorhombic unit cell.
FIG. 9. X-ray diffraction pattern at room temperature for x
= 0.10. The inset shows details in the range 40° 艋 2␪ 艋 46°. The
crystal structure is 14M with a monoclinic unit cell.
structure is in between. Within the grains, the plates order
parallel as seen in Figs. 11共b兲 and 11共c兲. For the case of the
L10 structure, the plates are not ordered.
IV. DISCUSSION
In the M共T兲 data of the sample with x = 0.13, two distinct
FM states with TCM ⬍ TCA for the martensitic and austenitic
phases can be observed. No long range ferromagnetism is
present in the temperature range TCM ⬍ T ⬍ TCA.
Two distinct FM states are also found for x = 0.15 that can
be evidenced in the M共H兲 data in Fig. 3共c兲. In this figure, it
is seen that below TCA, M共H兲 saturates above about 15 kOe.
However, the saturation magnetizations are smaller in the
range T ⬍ M s 共5 and 160 K兲 than for T ⬎ M s 共195 and
220 K兲. This is seen in more detail in Fig. 12, where M共T兲 in
high magnetic fields of 50 kOe is plotted. Starting from low
temperatures, M共T兲 decreases with increasing temperature
and conforms to a T3/2 Bloch law. The inset shows a linear
behavior of the T3/2 dependence of the reduced magnetiza-
FIG. 10. X-ray diffraction pattern at room temperature for x
= 0.10. The crystal structure is L10.
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MARTENSITIC TRANSITIONS AND THE NATURE OF…
TABLE III. Crystal structures and lattice parameters at room
temperature of the samples. The structure of the sample with x
= 0.10 is monoclinic with ␤ = 93.84°.
Lattice parameter
x
0.25
0.20
0.18
0.15
0.13
0.10
0.05
Crystal
structure
a共Å兲
b共Å兲
c共Å兲
L21
L21
L21
L21
10M
14M
L1
6.046
6.024
6.009
5.995
4.317
4.333
7.595
6.046
6.024
6.009
5.995
5.621
5.570
7.595
6.046
6.024
6.009
5.995
21.808
29.971
6.980
tion M / M 0, where M 0 is taken as the magnetization at T
= 5 K. Since Bloch behavior is valid essentially for T
⬍ TC / 3, TCM is expected to be virtual and lie around 600 K,
i.e., at a temperature higher than TCA. This property is also
found to be consistent with the concentration dependence of
the structural and magnetic phase transitions discussed below. The dashed line in Fig. 12 is a guide that represents the
behavior of M共T兲 beyond the stability range of the martensitic state.
A similar effect showing different magnetic exchange in
austenitic and martensitic states is encountered also in NiMn- Ga alloys.24,25 However, in these alloys, the ferromagnetic state in the martensitic phase has a higher magnetization than in the austenitic phase, and TCM is always greater
than TCA.
A feature that particularly stands out in the M共T兲 data of
the x = 0.15 and 0.13 samples is the pronounced increase in
the splitting between the ZFC and FC M共T兲 curves in the FM
martensitic state as opposed to the weak splitting in the FM
austenitic state. It is not possible from the present data to
give an exact account for such a large scale increase. The
rearrangement of the antiphase boundaries caused by the
twinning in the distorted martensitic state can have an influence on the Mn- Mn interatomic spacings so as to cause an
enhancement in the strength of the AF exchange. A closer
study of the martensitic structure is needed to clarify this
issue.
In the concentration range 8.0艋 e / a 艋 8.2, the
Ni0.50Mn0.50−xSnx system features diverse structural and magnetic transitions as seen in the phase diagram in Fig. 13. Data
from literature are also included in the diagram.19,21 TCA decreases slightly with increasing e / a up to e / a ⯝ 8.1. Above
this concentration, the system is in the martensitic state at
room temperature, and the Curie temperature, now TCM , decreases rapidly with increasing e / a. This sudden change in
the e / a dependence of the Curie temperature is attributed to
a change in the ferromagnetic exchange mechanism in the
martensitic phase with respect to that in the austenitic state.
The crystallographic distortion in the martensitic state evidently leads to an alteration in the band splitting of the electronic structure so as to cause a considerable change in the
FM ordering temperature. Using our present data and those
FIG. 11. Optical microscopy images of the microstructure for
x = 0.25 共L21兲, x = 0.13 共10M兲, x = 0.10 共14M兲, and x = 0.05 共L10兲.
of Ref. 19, we incorporate TCM into the phase diagram. TCM is
expected to vanish at about e / a = 8.2 共x = 0.10兲. If the line
describing TCM is extrapolated back to smaller e / a values, one
finds that for about x ⬍ 0.14, TCM ⬎ TCA. This provides support
for the validity of the argument given above for the values of
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PHYSICAL REVIEW B 72, 014412 共2005兲
KRENKE et al.
FIG. 14. ⌬S and ⌬H as a function of e / a.
FIG. 12. M共T兲 measured in 50 kOe. The dashed line is a guide
showing the expected behavior of M共T兲 of the martensitic state
beyond the stability range. The position of M s indicated in the figure is taken from the results of DSC measurements. The inset shows
the linear behavior of M / M 0 vs T3/2.
the Curie temperatures of the austenitic and martensitic
states for x = 0.15.
As the Sn concentration decreases, FM exchange weakens, and long range ferromagnetism no longer exists below
about x = 0.10. At lower Mn concentrations, the linear behavior of M共H兲 for x = 0.05 up to the highest magnetic fields
shows that AF exchange begins to dominate. However, a
Néel temperature cannot be identified in M共T兲 in the measured temperature range.
The enthalpy and entropy of the martensitic transition increase in absolute value with increasing e / a 共Fig. 14兲. The
increase in ⌬H is linear, while ⌬S shows a tendency to acquire a curvature at large e / a. The error bars are essentially
related to the uncertainties in positioning the base line of
dQ / dT in Fig. 6. An increase of ⌬S with increasing e / a has
also been reported for Ni- Mn- Ga alloys.26 This behavior is
in contrast to that observed in Cu-based alloys,27 for which
no significant e / a dependence of ⌬S is observed. For the
Cu-based alloys, ⌬S has mainly a vibrational contribution,
which is related to the low-lying transverse TA2 phonon
branch. It has been argued that for Ni- Mn- Ga, the electron
contribution to ⌬S is negligible and that the character of the
e / a dependence is related to a magnetic contribution that
relies on the difference in the magnetic exchange below and
above M s. The vibrational contribution was assumed to be
independent of e / a. Similar arguments could also apply for
Ni- Mn- Sn. In fact, in the case of Ni- Mn- Sn, the difference
in the magnetic exchange interactions below and above M s is
much larger than in Ni- Mn- Ga,28 as seen in Figs. 3 and 4.
Such a difference would account for the larger values found
in Ni- Mn- Sn when compared to those reported for NiMn- Ga. A detailed investigation aimed at separating the different contributions to the entropy change in magnetic shape
memory alloys would sustain the above arguments.
V. CONCLUSION
FIG. 13. The structural and magnetic transition temperatures as
a function of the valence electron concentration for Ni- Mn- Sn.
Optical microscopy and x-ray studies show that the type
of modulated structure of the martensite in Ni0.50Mn0.50−xSnx
014412-8
PHYSICAL REVIEW B 72, 014412 共2005兲
MARTENSITIC TRANSITIONS AND THE NATURE OF…
depends on the Sn composition. As the Sn concentration increases, the structure varies in a sequence 10M, 14M, and
L10. In the event that the austenitic and martensitic phases
are FM, the ferromagnetism of the parent and product phases
are found to be of a different nature, whereby each is characterized by a separate magnetic transition temperature. The
presence of ferromagnetism in the martensitic state is necessary for a magnetic shape memory effect to occur and is
found in the alloys with x = 0.13 and 0.15. However, whether
any magnetic shape memory effect occurs in these alloys is
*Electronic address: [email protected]
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yet to be demonstrated. The present study will be complimented by magnetostriction studies to address this question.
ACKNOWLEDGMENTS
We thank Peter Hinkel and Sabine Schremmer for technical support. This work was supported by Deutsche
Forschungsgemeinschaft 共GK277兲 and CICyT 共Spain兲,
Project No. MAT2004-1291. X.M. acknowledges support
from DGICyT 共Spain兲.
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